De Groot was given a yellow card for a high tackle on Adriaan Booysen inside the final 10 minutes with a ‘bunker’ review upgrading it to a red.
The All Blacks had recorded a bonus-point fourth try inside 25 minutes. They led 38-3 at half-time as Damien McKenzie and Cam Roigard crossed twice.
English referee Luke Pearce had initially given prop De Groot a yellow card after his shoulder caught the head of replacement Booysen in a lazy tackle.
But with no mitigation, his call was soon upgraded.
“We will have a look at it – there was a lot of shoulder on shoulder in that contact,” New Zealand head coach Ian Foster told BBC Radio 5 Live.
“We will compare it to something that happened yesterday and see what comes from it.”
On Thursday, France’s Romain Taofifenua avoided a red card for a high tackle, raising more questions about inconsistent decisions from officials at the Rugby World Cup.
New Zealand were on a two-match losing streak, having lost 35-7 to South Africa in a warm-up Test and seen their 31-match perfect record in World Cup pool stages come to an end against France seven days ago.
They made nine changes for their fixture in Toulouse and, as the rain hammered down, started fast with Roigard crossing inside 90 seconds.
The half-back added his second five minutes with before McKenzie went under the posts in the 20th minute and Leicester Fainga’anuku rode two tackles to score his side’s fourth.
McKenzie continued to dictate play and deservedly crossed for a second time before Lienert-Brown added a sixth try just before the break.
“We tried to establish ourselves up front and we got that dominance pretty early, which was key to the game,” added Foster.
“It allowed us to pick and choose how we played after that, but obviously we are delighted with the result and it is a step forward.”
Namibia tired in the second half, allowing De Groot, Dalton Papali’i and David Havili to add tries before the hour-mark.
Winger Caleb Clarke dived over in the 67th for try number 10, and, after being reduced to 14 players, the three-time winners continued to dominate as Rieko Ioane went over in the closing stages.
New Zealand’s win lifts them to second in Pool A. After a week off, they face Italy in their next match on 29 September.
It was a significant night for second row Sam Whitelock, who made his 148th New Zealand appearance to join Richie McCaw as the All Blacks’ most-capped player.
Le Roux Malan left the field with a serious looking knee injury in the first half Namibia, who lost 52-8 to Italy in their opener, have never won a match at a World Cup, losing 23 times since their debut in 1999.
Tiaan Swanepoel reduced their deficit to 12-3 in the opening 11 minutes with an assured penalty kick.
But the underdogs struggled in attack and a historic second-ever World Cup try against the All Blacks – having scored one in a loss in 2015 – never looked likely.
They face France in their next match in six days time before taking on Uruguay in their final Pool A fixture.
“We were up against a classy All Blacks side and with the pace they play at, it was quite tough for our boys,” said Namibia head coach Allister Coetzee.
“We have got France next and our World Cup is about our last game [against Uruguay]. We have to do better at set-piece and we have to get better at looking after the ball.”
The African side are likely to play the rest of the tournament without centre Le Roux Malan, who was carried off in the first half with a serious ankle injury.
Play was stopped for seven minutes before Malan left the field to applause from both sets of players and supporters inside Stadium de Toulouse.
